Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No: 020.00504
Autor: Erdös, Paul
Title: On sequences of integers no one of which divides the product of two others and on some related problems. (In English)
Source: Mitteil. Forsch.-Inst. Math. Mech. Univ. Tomsk 2, 74-82 (1938).
Review: The author defines an A sequence of integers as a sequence such that no member divides the product of any two other members. The number of integers less than n belonging to such a sequence is less than \pi (n)+O ({n^ 1/2 \over log n} )2. The number of integers less than n and belonging to a sequence such that the product of any two members is different from any other such product is less than \pi (n)+O (n^ 1/2). The error term in the latter formula cannot be better than O(n3/4 (log n)-3/2). It follows that, if p1 < p2 < ··· pz \leq n is an arbitrary sequence of primes such that z > (c1 n log log n) (log n)-2, where c1 is a sufficiently large constant, then the products (pi-1) (pj-1) cannot all be different.
Reviewer: Wright (Aberdeen)
Classif.: * 11B83 Special sequences of integers and polynomials
Index Words: Number theory